What is 2/31 divided by 2/21? (Answer: 21/31)

Exact Answer

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Problem: What is 2/31 divided by 2/21?
Formula / Expression: 2/31 ÷ 2/21
Final Answer: 21/31
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Step-by-Step Solution:

Step 1: Find the Reciprocal of the Second Fraction
Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 2/21 to get 21/2.
Working: 2/31 ÷ 2/21 = 2/31 × 21/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (31 × 2 = 62).
Working: 2 × 21/31 × 2 = 42/62

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 62, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/62 ÷ 2 = 21/31

Step 4: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 31 produces a repeating decimal (approximately 0.677419, or 67.7419%).
Working: 21 ÷ 31 = 0.677419 (67.7419%)

Key Values:
- Simplified Fraction: 21/31
- Mixed Number Form: 21/31
- Decimal Value: 0.677419
- Percentage: 67.7419%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-31-divided-by-2-21/
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2/31 ÷ 2/21 = 21/31

Simplified Fraction

21/31

Mixed Number

Proper (21/31)

Decimal Value

0.677419

Percentage

67.7419%

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Step-by-Step Solution: 2/31 ÷ 2/21

Step 1

Find the Reciprocal of the Second Fraction

Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 2/21 to get 21/2.

2/31 ÷ 2/21 = 2/31 × 21/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (31 × 2 = 62).

2 × 21/31 × 2 = 42/62

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 62, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/62 ÷ 2 = 21/31

Step 4

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 31 produces a repeating decimal (approximately 0.677419, or 67.7419%).

21 ÷ 31 = 0.677419 (67.7419%)

Visual Representation

The diagram below illustrates 2/31 divided by 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/31`
Mixed Number Form	`21/31`
Decimal Form	`0.677419`
Percentage	`67.7419%`

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Frequently Asked Questions

What is 2/31 divided by 2/21 as a fraction?

2/31 ÷ 2/21 in simplest fraction form is 21/31.

What is 2/31 divided by 2/21 as a decimal?

2/31 ÷ 2/21 converted to a decimal is 0.677419.

What is 2/31 divided by 2/21 as a percentage?

2/31 ÷ 2/21 expressed as a percentage is 67.7419%.

Does 2/31 divided by 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.677419...) because the denominator contains prime factors other than 2 and 5.